PLANE WAVE DISCONTINUOUS GALERKIN METHODS FOR THE 2D HELMHOLTZ EQUATION: ANALYSIS OF THE p-VERSION

被引：136

作者：

Hiptmair, R. ^{[1
]}

Moiola, A. ^{[1
]}

Perugia, I. ^{[2
]}

机构：

[1] ETH, SAM, CH-8092 Zurich, Switzerland

[2] Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2011年 / 49卷 / 01期

关键词：

Helmholtz equation; wave propagation; discontinuous Galerkin methods; plane waves; p-version error analysis; duality estimates; WEAK VARIATIONAL FORMULATION; LAGRANGE MULTIPLIERS; ELEMENT METHODS;

D O I：

10.1137/090761057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator -Delta-w(2), w > 0. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Despres, SIAM J. Numer. Anal., 35 (1998), pp. 255-299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of p-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121-136], and plane wave approximation theory.

引用

页码：264 / 284

页数：21

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